Engineering Mechanics Multiple Choice Questions on “Cartesian Vectors – 1”.
1. In right handed coordinate system which axis is considered to be positive?
a) The thumb is z-axis, fingers curled from x-axis to y-axis
b) The thumb is x-axis, fingers curled from z-axis to y-axis
c) The thumb is y-axis, fingers curled from x-axis to z-axis
d) The thumb is z-axis, fingers curled from y-axis to x-axis
Answer: a
Clarification: As right handed coordinate system means that you are curling your fingers from positive x-axis towards y-axis and the thumb which is projected is pointed to the positive z-axis. Thus visualizing the same and knowing the basic members of the axis will not create many problems.
2. If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector?
a) B units
b) A units
c) C units
d) Square root of a sum of squares of the three, i.e. A, B and C
Answer: a
Clarification: As the given vector is shown in the Cartesian system, the number with “j” is the Y-axis component of the given vector. With the numbers with “i” representing components of x-axis and “k” representing the z axis respectively.
3. If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?
a) Xi + Yj + Zk
b) Yi + Xj + Zk
c) Zi + Yj + Xk
d) Zi + Xj + Yk
Answer: d
Clarification: It is given that x, y and z-axis components are Z, X and Y respectively. Thus, just by placing the right coordinates we get option d to be correct. Here just the interchange of the axis’s representor with their respective axis is creating confusion. Which must be figured out.
4. Which statement is right for force vector F = Ai + Bj + Ck?
a) In rectangular components representation of any vector we have vector F = Ai + Bj + Ck
b) In rectangular components representation of any vector we have vector F = Ax + By + Cz
c) In rectangular components representation of any vector we have vector F = Fx + Fy + Fz
d) In rectangular components representation of any vector we have vector F = Fi + Fj + Fk
Answer: c
Clarification: As given the vector is F = Ai + Bj + Ck, this implies that the x ,y and z-axis components of this vector is A, B and C respectively. But, in rectangular components representation of any vector, the vector is written as F = Fx + Fy + Fz.
5. What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C?
a) Square root of the squares each A, B and C
b) Square of the squares each A, B and C
c) Cube root of the squares each A, B and C
d) Cube of the squares each A, B and C
Answer: a
Clarification: The magnitude of a Cartesian vector having the x, y and z axis components to be A, B and C is always the square root of the squares each A, B and C. This comes from the distance formula between two points in the Cartesian plane. That is the square root of the subtraction of the final and initial point of a line.
6. What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively)?
a) B/F
b) C/F
c) A/F
d) 1
Answer: c
Clarification: The cosine component of the vector is defined as the ratio of the x-axis component to the magnitude of the vector, i.e. F in this case. Likewise, the sine component is the ratio of the y-axis component to the magnitude of the vector.
7. What is the sum of squares of the cosine angles made by the force vector with the coordinate axis?
a) 1
b) ½
c) 2
d) 3
Answer: a
Clarification: The sum of the squares of the cosines of the vector will give you the squares of the components in the numerator, and the vector’s magnitude’s square in the denominator. But the numerator sum is equal to the vector’s magnitude’s square. Thus, the answer = 1.
8. What is the x-axis component of the force vector Ai + Bj +Ck with magnitude equal to F?
a) B
b) C
c) Fcosα
d) Fcosβ
